[1]曾文平.四阶抛物型方程的一族高精度恒稳的差分格式[J].华侨大学学报(自然科学版),2003,24(3):245-248.[doi:10.3969/j.issn.1000-5013.2003.03.004]
　Zeng Wenping.A Family of Highly Accurate and Absolutely Stable Difference Schemes for Solving Parabolic Equation of Four Order[J].Journal of Huaqiao University(Natural Science),2003,24(3):245-248.[doi:10.3969/j.issn.1000-5013.2003.03.004]
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四阶抛物型方程的一族高精度恒稳的差分格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第24卷
期数:
2003年第3期
页码:
245-248
栏目:
出版日期:
2003-07-20

文章信息/Info

Title:
A Family of Highly Accurate and Absolutely Stable Difference Schemes for Solving Parabolic Equation of Four Order
文章编号:
1000-5013(2003)03-0245-04
作者:
曾文平
华侨大学数学系 福建泉州362011
Author(s):
Zeng Wenping
Dept. of Math., Huaqiao Univ., 362011, Quanzhou, China
关键词:
四阶抛物型方程;  绝对稳定;  高精度;  隐式差分格式
Keywords:
parabolic equation of four order;  absolutely slable;  high accuracy;  implicit difference scheme
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2003.03.004
文献标志码:
A
摘要:
对四阶抛物型方程 u t+ 2 u x4=0构造出一族截断误差阶为 O((Δt) 2 +(Δx) 6)的三层隐式差分格式 .证明它是绝对稳定的,且可用追赶法求解 .数值例子表明,文中所提出的格式是有效的,理论分析与实际计算相吻合 .
Abstract:
A family of three layered, implicit differance schemes with the truncation error in the order of O ((Δ t ) 2+(Δ x ) 6) are constructed for solving parabolic equation of four order. They are proved to be absolutely stable and they can be solved by double sweeping method. As indicated by numerical example, the schemes presented here are effective; and theoretical analysis coincides with actual computation.

参考文献/References:

[1] 萨乌里耶夫ВК, 袁兆鼎. 抛物型方程的网格积分法 [M]. 北京:科学出版社, 1963.34-166.
[2] Richtrnger R D, Morton K W. Difference method for initial-value problems [M]. New York:Wiley, 1967.
[3] MILLER J J H. On the location of zeros of certain classes of polynomials with application to numerical analysis [J]. Journal of the Institute of Mathematics and Its Applications, 1971(1):394-406.

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备注/Memo

备注/Memo:
华侨大学科研基金资助项目(01HZR04)
更新日期/Last Update: 2014-03-23